It was summer - but dry in Europe isn't dry like the Ukraine. There's lots of rain - that's why this is some of the most fertile land on earth. But it certainly wasn't like a Northern European winter where mud is almost as bad as in Poland. I'd say you have a lot of latitude - might want some splattered mud and some soil pressed into the tracks. Obviously there'd always be a lot of dirt beneath the fenders and some kind of dust or dirt covering. No clean tanks. None. The thing I would keep in mind is that allied tanks in Normandy would probably have been pretty new, and there was a lot of hurry up and wait. My opinion only of course, but I'd think dirt, mud, dust, rain marks etc, but take it easy on chipping. (Obviously you could always put on battle damage - didn't take long for a AFV to be in a mortar or artillery barrage, not to mention MG fire. And I'd guess there would be lots of places to bend something.)
If you're thinking of the Longest Day GB better check with the boss. The period is supposed to end on July 1 - Falaise was about a month later. I was going to model a Free French Sherman but was over ruled.
Eric